Inequalities and Their Graphs

This video covers lessons 2.4 and 2.5 on inequalities, focusing on solving inequalities, including word problems and complex examples. It introduces compound inequalities, explaining how to solve and graph them. The video emphasizes understanding inequality symbols, solving techniques, and graphing methods, providing practical examples and shortcuts for efficient problem-solving.

What does the inequality 2x < 10 represent?

• x is less than 5

• x is greater than 10

• x is less than 10

• x is greater than 5

If Dave has $15 to spend on an $8 book and two birthday cards, how much can he spend on each card?

• $4.00

• $3.50

• $2.50

• $5.00

What is the solution to the inequality -1/2x < -23/2?

• x < -23

• x > -23

• x < 23

• x > 23

How many cubic meters of gravel can a crane lift if it can support a maximum load of 15,000 kg, and the bucket weighs 2,000 kg?

• 7.5 cubic meters

• 8.6 cubic meters

• 9.0 cubic meters

• 10.0 cubic meters

If a student has 60 minutes to practice piano and wants to spend at least 35 minutes playing songs, how much time can he spend on each of the 5 scales?

• 15 minutes or less

• 10 minutes or less

• 20 minutes or less

• 5 minutes or less

What does it mean when a graph of an inequality uses the word 'and'?

• The graph is a curve

• The graph is a straight line

• The graph goes apart

• The graph comes together

In a compound inequality, what does an open circle on the graph indicate?

• The value is included

• The value is negative

• The value is zero

• The value is not included

What is the correct inequality for a temperature range between 70 and 95 degrees inclusive?

• 70 ≥ T ≥ 95

• 70 < T < 95

• 70 ≤ T ≤ 95

• 70 > T > 95

Which of the following is a shortcut for identifying an 'or' inequality on a graph?

• The graph is a straight line

• The graph is a curve

• The graph goes apart with open circles

• The graph comes together with closed circles

What is the solution to the inequality 4x + 3 > 23?

• x > 4

• x < 4

• x < 5

• x > 5